Simple interest is where the amount of interest earned is fixed over time. For example, if you saved ₹1000 at 4% simple interest you would earn ₹40 per year, every year. The amount of interest earned stays the same when dealing with simple interest.
Simple Interest = Principal x Interest Rate x Term of the loan
= P x i x n
Example:
Suppose $1,000 were invested on January 1, 2010 at 10% simple interest rate for 5 years. Calculate the total simple interest on the amount. Solution We have, Principle P =$1,000
Interest Rate      i  = 10% per year = 0.1
Time                t  = 5 years
Simple Interest     Is = $1,000 × 0.1 × 5 =$500

Compound interest is where interest is paid on the amount already earned leading to greater and greater amounts of interest. For example ₹1000 at 4% compound interest would earn you ₹40 in the first year but in the second year you would earn 4% on the new amount of ₹1040 which would be ₹41.60.

A formula for calculating annual compound interest is as follows:

$S = P \left(1 + \frac{j}{n}\right)^{nt}$
Where,
·         S = value after t periods
·         P = principal amount (initial investment)
·         j = annual nominal interest rate (not reflecting the compounding)
·         n = number of times the interest is compounded per year
·         t = number of years the money is borrowed for

Example:
Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly

Explanation:

Amount=16000(1+5100)3= 18522C.I.  =1852216000=2522